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View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:1. Ordinary Differential Equations
Subcategory:1.2. Second-Order Linear Equations
Equation(s):$\displaystyle (c_4x^4+c_3x^3+c_2x^2)y''_{xx}+(b_3x^3+b_2x^2+b_1x+b_0)y'_{x}+(a_2x^2+a_1x+a_0)y=0$\hfill\break
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle y(x)=1-\frac{a_0}{b_0}x+\left[\frac{a_0(b_1+a_0)}{2b_0^2}-\frac{a_1}{2b_0}\right]x^2$,\hfill\break
where\\
$a_0,a_1,b_0,b_1,b_3,c_3,c_4$ arbitrary constants\\
$b_0\neq0$\\
$a_1\neq \frac{a_0(a_0+b_1)}{b_0}$\\
$a_2=-2c_4-2b_3$\\
$b_2=-\frac{2c_3+a_1}{2}+\frac{b_0a_0(b_3+a_2)}{a_0(b_1+a_0)-a_1b_0}$\\
$c_2=-\frac{2b_1+a_0}{2}+\frac{b_0a_0(b_2+a_1)-a_2b_0}{a_0(b_1+a_0)-a_1b_0}$\\
Novelty:New solution(s) / integral(s)
Author/Contributor's Details
Last name:Stepuchev
First name:Valeriy
Country:Latvija
City:Sigulda
Statistic information
Submission date:Mon 27 Sep 2010 19:39
Edits by author:0

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